1,544 research outputs found

    Self-stabilizing algorithms for Connected Vertex Cover and Clique decomposition problems

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    In many wireless networks, there is no fixed physical backbone nor centralized network management. The nodes of such a network have to self-organize in order to maintain a virtual backbone used to route messages. Moreover, any node of the network can be a priori at the origin of a malicious attack. Thus, in one hand the backbone must be fault-tolerant and in other hand it can be useful to monitor all network communications to identify an attack as soon as possible. We are interested in the minimum \emph{Connected Vertex Cover} problem, a generalization of the classical minimum Vertex Cover problem, which allows to obtain a connected backbone. Recently, Delbot et al.~\cite{DelbotLP13} proposed a new centralized algorithm with a constant approximation ratio of 22 for this problem. In this paper, we propose a distributed and self-stabilizing version of their algorithm with the same approximation guarantee. To the best knowledge of the authors, it is the first distributed and fault-tolerant algorithm for this problem. The approach followed to solve the considered problem is based on the construction of a connected minimal clique partition. Therefore, we also design the first distributed self-stabilizing algorithm for this problem, which is of independent interest

    Universal Loop-Free Super-Stabilization

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    We propose an univesal scheme to design loop-free and super-stabilizing protocols for constructing spanning trees optimizing any tree metrics (not only those that are isomorphic to a shortest path tree). Our scheme combines a novel super-stabilizing loop-free BFS with an existing self-stabilizing spanning tree that optimizes a given metric. The composition result preserves the best properties of both worlds: super-stabilization, loop-freedom, and optimization of the original metric without any stabilization time penalty. As case study we apply our composition mechanism to two well known metric-dependent spanning trees: the maximum-flow tree and the minimum degree spanning tree

    Self-Stabilizing Distributed Cooperative Reset

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    Self-stabilization is a versatile fault-tolerance approach that characterizes the ability of a system to eventually resume a correct behavior after any finite number of transient faults. In this paper, we propose a self-stabilizing reset algorithm working in anonymous networks. This algorithm resets the network in a distributed non-centralized manner, i.e., it is multi-initiator, as each process detecting an inconsistency may initiate a reset. It is also cooperative in the sense that it coordinates concurrent reset executions in order to gain efficiency. Our approach is general since our reset algorithm allows to build self-stabilizing solutions for various problems and settings. As a matter of facts, we show that it applies to both static and dynamic specifications since we propose efficient self-stabilizing reset-based algorithms for the (1-minimal) (f, g)-alliance (a generalization of the dominating set problem) in identified networks and the unison problem in anonymous networks. Notice that these two latter instantiations enhance the state of the art. Indeed, in the former case, our solution is more general than the previous ones, while in the latter case, the complexity of our unison algorithm is better than that of previous solutions of the literature

    Self-Stabilizing Construction of a Minimal Weakly ST\mathcal{ST}-Reachable Directed Acyclic Graph

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    We propose a self-stabilizing algorithm to construct a minimal weakly ST\mathcal{ST}-reachable directed acyclic graph (DAG), which is suited for routing messages on wireless networks. Given an arbitrary, simple, connected, and undirected graph G=(V,E)G=(V, E) and two sets of nodes, senders S(V)\mathcal{S} (\subset V) and targets T(V)\mathcal{T} (\subset V), a directed subgraph G\vec{G} of GG is a weakly ST\mathcal{ST}-reachable DAG on GG, if G\vec{G} is a DAG and every sender can reach at least one target, and every target is reachable from at least one sender in G\vec{G}. We say that a weakly ST\mathcal{ST}-reachable DAG G\vec{G} on GG is minimal if any proper subgraph of G\vec{G} is no longer a weakly ST\mathcal{ST}-reachable DAG. This DAG is a relaxed version of the original (or strongly) ST\mathcal{ST}-reachable DAG, where every target is reachable from every sender. This is because a strongly ST\mathcal{ST}-reachable DAG GG does not always exist; some graph has no strongly ST\mathcal{ST}-reachable DAG even in the case S=T=2|\mathcal{S}|=|\mathcal{T}|=2. On the other hand, the proposed algorithm always constructs a weakly ST\mathcal{ST}-reachable DAG for any S|\mathcal{S}| and T|\mathcal{T}|. Furthermore, the proposed algorithm is self-stabilizing; even if the constructed DAG deviates from the reachability requirement by a breakdown or exhausting the battery of a node having an arc in the DAG, this algorithm automatically reconstructs the DAG to satisfy the requirement again. The convergence time of the algorithm is O(D)O(D) asynchronous rounds, where DD is the diameter of a given graph. We conduct small simulations to evaluate the performance of the proposed algorithm. The simulation result indicates that its execution time decreases when the number of sender nodes or target nodes is large

    Algorithmes auto-stabilisants pour la construction de structures couvrantes réparties

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    This thesis deals with the self-stabilizing construction of spanning structures over a distributed system. Self-stabilization is a paradigm for fault-tolerance in distributed algorithms. It guarantees that the system eventually satisfies its specification after transient faults hit the system. Our model of distributed system assumes locally shared memories for communicating, unique identifiers for symmetry-breaking, and distributed daemon for execution scheduling, that is, the weakest proper daemon. More generally, we aim for the weakest possible assumptions, such as arbitrary topologies, in order to propose the most versatile constructions of distributed spanning structures. We present four original self-stabilizing algorithms achieving k-clustering, (f,g)-alliance construction, and ranking. For every of these problems, we prove the correctness of our solutions. Moreover, we analyze their time and space complexity using formal proofs and simulations. Finally, for the (f,g)-alliance problem, we consider the notion of safe convergence in addition to self-stabilization. It enforces the system to first quickly satisfy a specification that guarantees a minimum of conditions, and then to converge to a more stringent specification.Cette thèse s'intéresse à la construction auto-stabilisante de structures couvrantes dans un système réparti. L'auto-stabilisation est un paradigme pour la tolérance aux fautes dans les algorithmes répartis. Plus précisément, elle garantit que le système retrouve un comportement correct en temps fini après avoir été perturbé par des fautes transitoires. Notre modèle de système réparti se base sur des mémoires localement partagées pour la communication, des identifiants uniques pour briser les symétries et un ordonnanceur inéquitable, c'est-à-dire le plus faible des ordonnanceurs. Dans la mesure du possible, nous nous imposons d'utiliser les plus faibles hypothèses, afin d'obtenir les constructions les plus générales de structures couvrantes réparties. Nous présentons quatre algorithmes auto-stabilisants originaux pour le k-partitionnement, la construction d'une (f,g)-alliance et l'indexation. Pour chacun de ces problèmes, nous prouvons la correction de nos solutions. De plus, nous analysons leur complexité en temps et en espace à l'aide de preuves formelles et de simulations. Enfin, pour le problème de (f,g)-alliance, nous prenons en compte la notion de convergence sûre qui vient s'ajouter à celle d'auto-stabilisation. Elle garantit d'abord que le comportement du système assure rapidement un minimum de conditions, puis qu'il continue de converger jusqu'à se conformer à une spécification plus exigeante

    Self-stabilizing k-clustering in mobile ad hoc networks

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    In this thesis, two silent self-stabilizing asynchronous distributed algorithms are given for constructing a k-clustering of a connected network of processes. These are the first self-stabilizing solutions to this problem. One algorithm, FLOOD, takes O( k) time and uses O(k log n) space per process, while the second algorithm, BFS-MIS-CLSTR, takes O(n) time and uses O(log n) space; where n is the size of the network. Processes have unique IDs, and there is no designated leader. BFS-MIS-CLSTR solves three problems; it elects a leader and constructs a BFS tree for the network, constructs a minimal independent set, and finally a k-clustering. Finding a minimal k-clustering is known to be NP -hard. If the network is a unit disk graph in a plane, BFS-MIS-CLSTR is within a factor of O(7.2552k) of choosing the minimal number of clusters; A lower bound is given, showing that any comparison-based algorithm for the k-clustering problem that takes o( diam) rounds has very bad worst case performance; Keywords: BFS tree construction, K-clustering, leader election, MIS construction, self-stabilization, unit disk graph

    Self-* distributed query region covering in sensor networks

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    Wireless distributed sensor networks are used to monitor a multitude of environments for both civil and military applications. Sensors may be deployed to unreachable or inhospitable areas. Thus, they cannot be replaced easily. However, due to various factors, sensors\u27 internal memory, or the sensors themselves, can become corrupted. Hence, there is a need for more robust sensor networks. Sensors are most commonly densely deployed, but keeping all sensors continually active is not energy efficient. Our aim is to select the minimum number of sensors which can entirely cover a particular monitored area, while remaining strongly connected. This concept is called a Minimum Connected Cover of a query region in a sensor network. In this research, we have designed two fully distributed, robust, self-* solutions to the minimum connected cover of query regions that can cope with both transient faults and sensor crashes. We considered the most general case in which every sensor has a different sensing and communication radius. We have also designed extended versions of the algorithms that use multi-hop information to obtain better results utilizing small atomicity (i.e., each sensor reads only one of its neighbors\u27 variables at a time, instead of reading all neighbors\u27 variables). With this, we have proven self-* (self-configuration, self-stabilization, and self-healing) properties of our solutions, both analytically and experimentally. The simulation results show that our solutions provide better performance in terms of coverage than pre-existing self-stabilizing algorithms
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